yes  interval is -------( 2n pi - pi/3, 2npi + pi/3)--------

its correct

inverse sin is defined for [-1,1] and range of secx is (-infinity,-1) U (1,infinity)

so [secx] can only assume values of -1 and 1 if the inverse of sin is to be defined.

i.e. secx belongs to {-1} U (1,2)

x belongs to (2npi - pi/3, 2npi + pi/3)